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refusez aux deux lignes droites, même prolongées à l’infini, le pouvoir d’enclore un espace. Vous n’avez pas besoin pour cela de les suivre à l’infini, vous n’avez qu’à vous transporter par l’imagination à l’endroit où elles convergent, et vous avez à cet endroit l’impression d’une ligne qui se courbe, c’est-à-dire qui cesse d’être droite[1]. Cette présence imaginaire tient lieu
- ↑ For though, in order actually to see that two given lines never meet, it would be necessary to follow them to infinity ; yet without doing so, we may know that if they ever do meet, or if, after diverging from one another, they begin again to approach, this must take place not at an infinite, but at a finite distance. Supposing, therefore, such to be the case, we can transport ourselves thither in imagination, and can frame a mental image of the appearance which one or both of the lines must present at that point, which we may rely on as being precisely similar to the reality. Now, whether we fix our contemplation upon this imaginary picture, or call to mind the generalizations we have had occasion to make from former ocular observation, we learn by the evidence of experience, that a line which, after diverging from another straight line, begins to approach to it, produces the impression on our senses which we describe by the expression “a bent line”, not by the expression, “a straight line”.
